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Quantitative Aptitude

AVERAGES MCQs

Averages

Total Questions : 3752 | Page 8 of 376 pages
Question 71.

In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

  1.    65 kgs
  2.    67 kgs
  3.    69 lgs
  4.    70 kgs
  5.    None of these
 Discuss Question
Answer: Option B. -> 67 kgs
 -  Let Arun's weight by X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70.
According to Arun's mohter, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
           Required average =   66 + 67 + 68   =   201   = 67 kg. 3 3
Question 72.

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:

  1.    21
  2.    22
  3.    23
  4.    24
  5.    None of these
 Discuss Question
Answer: Option A. -> 21
 -  Let the total number of workers be x. then,
8000x = (12000 x 7) + 6000 (x – 7)
2000x = 4200
x = 21
Question 73.

In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65, How many papers were there in the examination?

  1.    10
  2.    11
  3.    12
  4.    13
  5.    None of these
 Discuss Question
Answer: Option B. -> 11
 -  Let the number of papers be x.
Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11
Question 74.

16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B?

  1.    77 1/3
  2.    77 2/3
  3.    75 1/3
  4.    75 2/3
  5.    None of these
 Discuss Question
Answer: Option B. -> 77 2/3
 -   Average  = (76 x 16) - (75 x 10) 6       =   1216 - 750 6           = 466 6         = 233 3         = 77 2 3  
Question 75.

The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:

  1.    30.5
  2.    36.5
  3.    37
  4.    39.5
  5.    None of these
 Discuss Question
Answer: Option B. -> 36.5
 -  Correct sum = (36 x 50 + 48 – 23) = 1825
 
Correct mean =  
1825 50  
= 36.5
Question 76.

The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one them weighing 65 kg. What might be the weight of the new person?

  1.    65 kg
  2.    75 kg
  3.    85 kg
  4.    90 kg
  5.    None of these
 Discuss Question
Answer: Option C. -> 85 kg
 -  Total weight increased = (8 x 2.5) kg = 20 kg
Weight of new person = (65 + 20) kg = 85 kg
Question 77.

The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is:

  1.    51.4
  2.    53.6
  3.    54.4
  4.    55.6
  5.    None of these
 Discuss Question
Answer: Option A. -> 51.4
 -  Let the required mean score be a
Then, 20 x 80 + 25 x 31 + 55 x a = 52 x 100
1600 + 775 + 55a = 5200
55a = 2825
a = 51.4
Question 78.

The average of a non-zero number and its square is 5 times the number. The number is:

  1.    0 , 9
  2.    0 , 8
  3.    5 , 8
  4.    6 , 0
  5.    None of these
 Discuss Question
Answer: Option A. -> 0 , 9
 -  Let the number be x.
Then,
x + x2 2 = 5x       x2 - 9x = 0   x (x - 9) = 0   x = 0 or x = 9.
Question 79.

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:

  1.    3 M x M
  2.    3 M
  3.    9 M
  4.    9 M x M
  5.    None of these
 Discuss Question
Answer: Option A. -> 3 M x M
 -   We have :   a + b + c 3   = M or (a + b + c) = 3M.       Now, (a + b + c)M2 = (3M)M2 = 9M2       a2 + b2 + c2 + 2 (ab + bc + ca) = 9M2           a2 + b2 + c2 = 9M2         Required mean =   a2 + b2 + c2 3   = 9M2 3 = 3M2
Question 80.

3 year ago, the average of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:

  1.    1 year
  2.    2 years
  3.    3 years
  4.    4 years
  5.    None of these
 Discuss Question
Answer: Option B. -> 2 years
 -  Total age of 5 members, 3 years ago = (17 x 5) years = 85 years
Total age of 5 members now = (85 + 3 x 5) years = 100 years
Total age of 6 members now = (17 x 6) years = 102 years
Age of the baby = (102 – 100) years = 2 years

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